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More on changing response propensities

I've been thinking some more about this issue. A study that I work on monitors the estimated mean response propensities every day. The models are refit each day and the estimates updated. The mean estimated propensity of the active cases for each day is then graphed. Each day they decline.

The study has a second phase. In the second, phase, the response probabilities start to go up. Olson and Groves wrote a paper using these data. They argue that the changed design has changed the probabilities of response. I agree with that point of view in this case.

But I also recently finished a paper that looked at the stability of the estimated coefficients over time from models that are fit daily on an ever increasing dataset. The coefficients become quite stable after the first quarter. So the increase in probabilities in the second phase isn't due to changes in the coefficients.

The response probabilities we monitor don't account for the second phase (there's no predictor for that). They are based on call records.  So how does the propensity go up? More calling should only decrease the probability of response... unless some other things change. My hypothesis is that cases started to make more appointments in the second phase than before. There was more contact. In general, things that are evidence of an increasing probability of response and are also in the model started to happen. At some point, I'd like to look at the specifics of that.
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